Details

Time bar (total: 9.5s)

sample29.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify41.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
06025
129623
2171123
3500123

prune13.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 51.4b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
0.1b
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
39.9b
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
41.1b
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
14×associate-*l/
10×associate-/l*
9×associate-/r/ *-commutative
6×associate-*l* associate-/l/
5×div-inv
4×flip3-- flip-- fma-udef
3×frac-2neg clear-num
2×distribute-rgt-in distribute-lft-in times-frac associate-*r/
1×flip3-+ associate-/r* flip-+
Counts
4 → 40
Calls
4 calls:
13.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
11.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
15.0ms
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
19.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))

series3.5s

Counts
4 → 12
Calls
4 calls:
522.0ms
(* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta)))
269.0ms
(* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta)))
1.9s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
759.0ms
(/ (* i (+ (+ alpha beta) i)) (/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))

simplify55.0ms

Algorithm
egg-herbie
Counts
52 → 52
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0455755
12101692
25001656

prune216.0ms

Filtered
52 candidates to 44 candidates (84.6%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New47552
Fresh011
Picked101
Done000
Total48654

Merged error: 35.6b

Counts
54 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
9.9b
(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
27.9b
(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
39.2b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
97×frac-times
36×clear-num
35×frac-2neg
32×associate-*l/
31×flip3-+ flip-+
26×associate-/r*
19×associate-*r/
16×*-commutative
11×associate-*l*
6×associate-/r/
5×div-inv
4×+-commutative distribute-rgt-in associate-+l+ distribute-lft-in
1×associate-*r* un-div-inv
Counts
4 → 112
Calls
4 calls:
12.0ms
(* (* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
8.0ms
(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
4.0ms
(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

series1.2s

Counts
4 → 12
Calls
4 calls:
738.0ms
(* (* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
115.0ms
(* (/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (+ alpha beta) i))
143.0ms
(/ i (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
160.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

simplify117.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (96.0ms)

IterNodesCost
07752375
142692218
250012214

prune455.0ms

Filtered
124 candidates to 99 candidates (79.8%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1177124
Fresh505
Picked101
Done000
Total1237130

Merged error: 35.6b

Counts
130 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))
5.7b
(* (* i (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
35.7b
(/ (* (* i (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
39.2b
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
34×associate-*r/
20×frac-times
18×associate-/l/
14×associate-/r*
13×flip3-+ flip-+
12×*-commutative
10×clear-num
8×frac-2neg
5×associate-/l*
4×associate-*l* associate-*l/ div-inv
2×associate-*r* associate-/r/ un-div-inv fma-udef
1×pow2 distribute-rgt-in distribute-lft-in
Counts
4 → 59
Calls
4 calls:
2.0ms
(* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))
8.0ms
(* (* i (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
12.0ms
(/ (* (* i (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
3.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

series1.1s

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))
183.0ms
(* (* i (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
737.0ms
(/ (* (* i (+ (+ alpha beta) i)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))) (+ (- 1.0) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)))))
156.0ms
(/ (fma beta alpha (* i (+ (+ alpha beta) i))) (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))))

simplify56.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0392893
11861837
25001821

prune252.0ms

Filtered
71 candidates to 55 candidates (77.5%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New71071
Fresh066
Picked011
Done000
Total71778

Merged error: 35.6b

Counts
78 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ i (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
0.5b
(/ i (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)))
37.0b
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))
39.0b
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
20×associate-/r/
13×div-inv
9×frac-2neg clear-num
8×associate-/l*
7×associate-/r*
6×associate-/l/
4×times-frac
3×flip3-+ flip-+
2×*-commutative
Counts
4 → 42
Calls
4 calls:
8.0ms
(/ (/ i (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
4.0ms
(/ i (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)))
4.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))
4.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

series1.2s

Counts
4 → 12
Calls
4 calls:
767.0ms
(/ (/ i (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))) (/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i)))))
134.0ms
(/ i (/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i)))
153.0ms
(/ (fma (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta)) (- 1.0)) (+ (+ alpha beta) i))
139.0ms
(/ (* (fma i 2.0 (+ alpha beta)) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))

simplify38.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0304602
11331593
25002584

prune155.0ms

Filtered
54 candidates to 42 candidates (77.8%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New52254
Fresh235
Picked011
Done011
Total54761

Merged error: 35.6b

Counts
61 → 7

regimes146.0ms

Accuracy

43% (2.2b remaining)

Error of 38.0b against oracle of 35.8b and baseline of 39.6b

bsearch82.0ms

Steps
ItersRangePoint
10
1.1695770500521425e+157
2.6251527105369915e+169
1.183331871632842e+157

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03233
13233

end0.0ms

sample672.0ms

Algorithm
intervals
Results
359.0ms8000×body80valid
129.0ms8000×pre80true